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Highly irregular serial correlation tests

Author

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  • Amengual, Dante
  • Bei, Xinyue
  • Sentana, Enrique

Abstract

Tests are developed for neglected serial correlation when the information matrix is repeatedly singular under the null hypothesis. Specifically, consideration is given to white noise against a multiplicative seasonal Ar model, and a local-level model against a nesting Ucarima one. The proposed tests, which involve higher-order derivatives, are asymptotically equivalent to the likelihood ratio test but only require estimation under the null. It is shown that the tests effectively check that certain autocorrelations of the observations are zero, so their asymptotic distribution is standard. Monte Carlo exercises examine finite sample size and power properties, with comparisons made to alternative approaches.

Suggested Citation

  • Amengual, Dante & Bei, Xinyue & Sentana, Enrique, 2026. "Highly irregular serial correlation tests," Econometrics and Statistics, Elsevier, vol. 39(C), pages 4-21.
    • Handle: RePEc:eee:ecosta:v:39:y:2026:i:c:p:4-21
    DOI: 10.1016/j.ecosta.2024.01.001
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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